I have to disagree with the rest of the thread, unfortunate or not. I now choose HR every time.
For the record, I stay in Chicago at least once a month and have stayed at all of the locations within 1 mile of Michigan Ave.
The Hyatt on Mag Mile, although close to Michigan Ave, it is not
much closer to Michigan Ave to make a difference. Maybe this is also because I love to walk, so it doesn't bother me to cross the river each time I need to go onto Michigan Ave. The strip and few blocks surrounding Mag Mile are often too crowded anyway and I will Uber to surrounding pockets, etc for other dining options.
The service, rooms, and club are what make me return to the HR every month now. I've never had an issue getting an upgrade (I don't know if you have status) with a gorgeous view in a larger room. If there is a junior suite available when I check in, they have never had a problem transferring me. The club is currently under renovation, so it is in a larger suite on the 33rd floor, but it will be ready in 7 weeks. The Hyatt Mag Mile, while not having a club, does not have any rooms with tremendous views because they are not taller than any of the buildings surrounding them. Light is important to me, so I'd rather be starring at a river than Northwestern's medical building (you should request opposite, if you do stay).
BIG Bar has great servers and is a decent place to have drinks and/or some apps. It's a little on the pricey side (of course, no different at any of the others), but you pay for convenience.
The best part is that the HR is usually cheaper and you can get weekend rates right around the $100/night mark. This is because they have two towers of 34 floors each that they need to sell-out.
So maybe the HR isn't right in the heart of Mag Mile, but I like to say that it's my great little oasis away from the strip. A little more peaceful with my view of the river and less noise from Mag Mile.
I don't know if you will be driving out, but if you are, I can give you some ideas on cheaper options to park by either hotels!
Just have to be honest!
Regardless of where you stay (if you stay on Michigan), like someone said above me, you will probably take the L or a cab to Wrigleyville. I would say pick a location based on value and ease of transportation (whether you like to walk or not).
Edit: I didn't mention anything about HP River North! I don't think it's that exciting of a location or hotel for a tourist. About a 15-20 minute walk from the mile, depending how far north you want to go. You can take the L right on the corner of Illinois/Clark to get anywhere as well. Although, if you do not have status and want a free breakfast, this is the place for you as all Hyatt Place's feature free buffet-style breakfast.